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An athlete runs two rounds of a circular track of radius 45 m by exerting a force 1 of 200 N against the friction due to ground. Find the work done by him and justify your answer. using formula Work done=Force ×Displacement× Cos theta?
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An athlete runs two rounds of a circular track of radius 45 m by exert...
Understanding Work Done
Work done is defined as the product of the force applied, the displacement of the object, and the cosine of the angle between the force and the direction of displacement. The formula is expressed as:
Work Done = Force × Displacement × Cos(theta)
Key Parameters
- Force (F): 200 N (the force exerted by the athlete against friction)
- Displacement (d): The total distance covered by the athlete
- Radius of Track (r): 45 m
Calculating Displacement
To find the displacement for two rounds around a circular track, we first calculate the circumference of the track:
- Circumference (C) = 2 × π × r
- Circumference = 2 × π × 45 m ≈ 282.74 m
Since the athlete runs two rounds:
- Total Displacement (D) = 2 × C
- Total Displacement = 2 × 282.74 m ≈ 565.48 m
Angle Between Force and Displacement
In this scenario, the force exerted by the athlete (against friction) is in the opposite direction to the displacement, which means:
- Cos(theta) = Cos(180°) = -1
Calculating Work Done
Now, substituting values into the work done formula:
- Work Done = F × D × Cos(theta)
- Work Done = 200 N × 565.48 m × (-1)
Thus,
- Work Done = -113096 J
Conclusion
The negative sign indicates that the work done by the athlete is against the frictional force, meaning energy is expended in overcoming resistance. Therefore, the work done by the athlete is 113096 J (Joules).
Work done is defined as the product of the force applied, the displacement of the object, and the cosine of the angle between the force and the direction of displacement. The formula is expressed as:
Work Done = Force × Displacement × Cos(theta)
Key Parameters
- Force (F): 200 N (the force exerted by the athlete against friction)
- Displacement (d): The total distance covered by the athlete
- Radius of Track (r): 45 m
Calculating Displacement
To find the displacement for two rounds around a circular track, we first calculate the circumference of the track:
- Circumference (C) = 2 × π × r
- Circumference = 2 × π × 45 m ≈ 282.74 m
Since the athlete runs two rounds:
- Total Displacement (D) = 2 × C
- Total Displacement = 2 × 282.74 m ≈ 565.48 m
Angle Between Force and Displacement
In this scenario, the force exerted by the athlete (against friction) is in the opposite direction to the displacement, which means:
- Cos(theta) = Cos(180°) = -1
Calculating Work Done
Now, substituting values into the work done formula:
- Work Done = F × D × Cos(theta)
- Work Done = 200 N × 565.48 m × (-1)
Thus,
- Work Done = -113096 J
Conclusion
The negative sign indicates that the work done by the athlete is against the frictional force, meaning energy is expended in overcoming resistance. Therefore, the work done by the athlete is 113096 J (Joules).
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An athlete runs two rounds of a circular track of radius 45 m by exerting a force 1 of 200 N against the friction due to ground. Find the work done by him and justify your answer. using formula Work done=Force ×Displacement× Cos theta?
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An athlete runs two rounds of a circular track of radius 45 m by exerting a force 1 of 200 N against the friction due to ground. Find the work done by him and justify your answer. using formula Work done=Force ×Displacement× Cos theta? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about An athlete runs two rounds of a circular track of radius 45 m by exerting a force 1 of 200 N against the friction due to ground. Find the work done by him and justify your answer. using formula Work done=Force ×Displacement× Cos theta? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An athlete runs two rounds of a circular track of radius 45 m by exerting a force 1 of 200 N against the friction due to ground. Find the work done by him and justify your answer. using formula Work done=Force ×Displacement× Cos theta?.
An athlete runs two rounds of a circular track of radius 45 m by exerting a force 1 of 200 N against the friction due to ground. Find the work done by him and justify your answer. using formula Work done=Force ×Displacement× Cos theta? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about An athlete runs two rounds of a circular track of radius 45 m by exerting a force 1 of 200 N against the friction due to ground. Find the work done by him and justify your answer. using formula Work done=Force ×Displacement× Cos theta? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An athlete runs two rounds of a circular track of radius 45 m by exerting a force 1 of 200 N against the friction due to ground. Find the work done by him and justify your answer. using formula Work done=Force ×Displacement× Cos theta?.
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